Denote a point in the plane by z=(z,y) and a polynomial of nth degree in z by f(z) /spl Sigma//sub i,j//spl ges/o/sub 1/i+j/spl les(a/sub ij/x/sup i/y/sup j/). Denote by Z(f) the set of points for which f(z)=0. Z(f) is the 2D curve represented by f(z). In this paper, we present a new approach to fitting 2D curves to data in the plane (or 3D surfaces to range data) which has significant advantages over presently known methods. It requires considerably less computation and the resulting curve can be forced to lie close to the data set at prescribed points provided that there is an nth degree polynomial that can reasonably approximate the data. Linear programming is used to do the fitting. The approach can incorporate a variety of distance measures and global geometric constraints.
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机译:用z =(z,y)表示平面中的一个点,用f(z)/ spl Sigma // sub i,j // spl ges / o / sub 1 / i + j /表示z中的n次多项式spl les / n(a / sub ij / x / sup i / y / sup j /)。用Z(f)表示f(z)= 0的点集。 Z(f)是由f(z)表示的2D曲线。在本文中,我们提出了一种将2D曲线拟合到平面中的数据(或将3D曲面拟合到范围数据)的新方法,它比目前已知的方法具有明显的优势。如果存在第n次多项式可以合理地近似数据,则所需的计算量将大大减少,并且可以强制将所得曲线逼近指定点处的数据集。线性编程用于进行拟合。该方法可以合并各种距离度量和全局几何约束。
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